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- find the domain of He following function: fCx) = 5X -3メ -4 Q2, fom = [2x +H}, find f(-3.2) %3D Qi, Sketch the graph of Ha function y=-2 cos 4X + 3 Q4, Find the domain of Hu function fcw) =J 2x+3 -1Differentiate two ways: first, by using the Product Rule; then, by multiplying the expressions before differentiating. Compare your results as a check. Use a graphing calculator to check your results. 1. y = x°.x* 2. y = x³.x° 3. f(x) = (2x + 5)(3x – 4) 4. g(x) = (3x – 2)(4x + 1) 5. F(x) = 3x*(x² – 4x) %3D 6. G(x) = 4x²(x³ + 5x) 7. y = (3Vx + 2)x? 8. y = (4Vx + 3)x 9. f(x) = (2x + 5)(3x² – 4x + 1) 10. g(x) = (4x – 3)(2x2 + 3x + 5) 11. F(t) = (Vi + 2)(3t – 4Vi + 7) 12. G(t) = (2t + 3Vi + 5)(Vi + 4)The temperature in an auditorium is given by T = x² + y² - z. A mosquito located at (1,1,2) in the auditorium desires to fly in such a direction that it will get warm as soon as possible. In what direction must it fly?
- Find the equation of the tangent plane to the graph of 7y √x f(x, y) = at the point (4, -7). (Use symbolic notation and fractions where needed. Enter your answer using x-, y-, z-coordinates.) the equation:Find the points on the line 3x – 4y – 1 = 0 which are at a distance of 5 units from the point (3, 2).For what value(s) of a does the graph of f(x) = 2x + 3x? – 12x – 1 have a horizontal tangent line? Answer(s): 1 = • Use commas to separate your answers if you find multiple z-values.
- 3) Find the function of y= Jx. 1) Reflcct about the (2) Shift Up (3) Shift left 7units X-axis 8 Units2. (a) Let==1-i. (i) (ii) Plot the position of on an Argand Diagram. Express in the form = = ae¹b, where a, b e R, giving the exact value of a and the exact value of b. (b) Let w₁ = eix and w₂ = e¹(x-7), where x = R. (i) Find w₁+w₂ in the form e¹*(c +id). (ii) Hence find Re(w₁ + w₂) in the form A cos (x − a), where A >0 and 0
